Particulate filters are designed to remove soot from the exhaust flow of an engine, such as a diesel or gasoline internal combustion engine. When the accumulated soot reaches a predetermined amount, the filter is “regenerated” either actively, by burning off the accumulated soot, or passively, such as by the use of a catalyst. Mathematical and empirical soot models have been used to estimate the amount of soot present in the filter so that timely disposal or regeneration of the filter can be assured. One soot model predicts the amount of soot in the filter based on the pressure drop in exhaust flow through the filter (i.e., a differential pressure across the filter). Accuracy of the soot model used is important, as functioning of the particulate filter is impaired if the amount of soot present is too great. An inaccurate soot model also causes the filter to be regenerated at lower soot concentrations (grams of soot per volume of filter), which decreases fuel economy.
As passive regeneration increases, the accuracy of a differential pressure-based soot model decreases. In given temperature ranges and with given nitrogen dioxide levels in the exhaust flow, the level of passive regeneration increases, and pressure drop across the filter is not an accurate predictor of soot mass in the filter due to passive and nonhomogeneous burning of soot in the filter. Nonhomogeneous burning changes the soot distribution in the filter and therefore reduces the correlation between pressure drop over the filter and soot mass in the filter. For example, the nonhomogeneous burning causes cracks in the soot layer, reducing resistance to flow. Therefore, the pressure drop over the filter is less. If the model does not account for the effect of nonhomogeneous burning, then the model will predict a lower soot mass in the filter than actually exists.
During soot loading, some models attempt to correct a pressure drop-based model to account for nonhomogeneous burning due to passive regeneration by correlating the difference between measured soot mass (by weighing the filter) and predicted soot mass (based on pressure drop) with engine speed, engine fuel, and altitude as Nox concentration reaches a predetermined level.